The Justice League is a team comprised of the premier superheroes of the DC Universe, making them "The Worlds Greatest Superheroes". The current incarnation of the League bears resemblance to the original Silver Age Justice League of America but features updated versions of its cast of characters for the DC Universe's current "New 52" continuity.

I don't think they have one. Those huge personalities couldn't have one leader all the time, they do seem to sort of defer when necessary and other times they seem to come to a consensus without talking.

Now? Superman is kind of the figurehead, but Batman runs the show. Makes sense, Superman is the guy in the light that people look to, but Batman's pulling the strings from his shadow, it suits their characters. Before, Superman was the leader, but Batman and Wonder Women were his support. But DCnU, Superman seems less a figurehead, now that i think of it, but clearly not the leader. The public would not be privy to what the comic book readers are, so sure he might be the figurehead in the comic. Pre-52 Wonder Women was also a leader and figurehead to a degree, current is a grouped the rest of the league